SPM.1.AHL.TZ0.17

pestleMathematicsAIHLPaper 1SPM· sl-4-8-binomial-distributionsource ↗

Mr Burke teaches a mathematics class with 15 students. In this class there are 6 female students and 9 male students.

Each day Mr Burke randomly chooses one student to answer a homework question.

In the first month, Mr Burke will teach his class 20 times.

Find the probability he will choose a female student 8 times.

[2]

The Head of Year, Mrs Smith, decides to select a student at random from the year group to read the notices in assembly. There are 80 students in total in the year group. Mrs Smith calculates the probability of picking a male student 8 times in the first 20 assemblies is 0.153357 correct to 6 decimal places.

Find the number of male students in the year group.

[4]

Markscheme / solution

P(X = 8) (M1)

Note: Award (M1) for evidence of recognizing binomial probability. eg, P(X = 8), X ∼ B $\left( {20,\,\frac{6}{{15}}} \right)$ .

= 0.180 (0.179705…) A1

[2 marks]

let $x$ be the number of male students

recognize that probability of selecting a male is equal to $\frac{x}{{80}}$ (A1)

$\left( {{\text{set up equation}}\,{}^{20}{{\text{C}}_8}{{\left( {\frac{x}{{80}}} \right)}^8}{{\left( {\frac{{80 - x}}{{80}}} \right)}^{12}} = } \right)\,0.153357$ (M1)

number of male students = 37 (M1)A1

Note: Award (M1)A0 for 27.

[4 marks]

Examiners’ report

[N/A]